Where do philosophers appeal to intuitions (if they do)?

It might be that intuitions are central to philosophy, and it might be that this is true because when philosophers give case-based arguments for philosophical claims (in published philosophy), the case verdict is typically (a) an intuited proposition and (b) either left undefended or defended on the grounds that it is an intuited proposition. This paper remains neutral on these global issues, however, and instead focuses on whether there is a nontrivial (or many-membered) class of case-based arguments in philosophy in which the case verdict is defended by appeal to background beliefs and not on the grounds that it is an intuited proposition. The paper argues that the answer is affirmative by examining seven such arguments that are referred to as “paradigm cases” of case-based arguments in which the verdict is justified via an appeal to intuition.